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C₂×#2746 #52182

• p-group
• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

1219 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 26 points:

(1,2);(3,4)(5,9)(6,7)(8,10)(11,12,15,17)(13,18,14,16)(19,20)(21,24)(22,26)(23,25);(4,7)(8,9)(11,13,15,14)(12,16,17,18)(19,21,23,26)(20,24,25,22);(3,5,6,10)(4,8,7,9)(11,14,15,13)(12,16,17,18)(19,21)(20,22)(23,26)(24,25);(3,4)(5,8)(6,7)(9,10)(11,12)(13,18)(14,16)(15,17)(19,22)(20,21)(23,24)(25,26)

Conjugacy classes & character table

64 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(256, 45170);